Find the coefficient of the given term in the binomial expansion.
-$x ^ { 7 }$ term, $( x - 2 ) ^ { 12 }$
A) $- 25,344$
B) 25,344
C) $- 127,733,760$
D) 792

Question

Quizplus · Accepted Answer

The coefficient of $x^7$ in the expansion of $(x - 2)^{12}$ can be found using the binomial theorem, specifically the term is given by $\binom{n}{k} \cdot a^{n-k} \cdot b^k$ where $n=12$, $k=12-7=5$, $a=x$, and $b=-2$. Thus, the coefficient is $\binom{12}{5} \cdot (-2)^5 = 792 \cdot -32 = -25,344$.

Find the Coefficient of the Given Term in the Binomial x7x ^ { 7 }x7

Find the Coefficient of the Given Term in the Binomial $x ^ { 7 }$